How to make a camera rotate on the spot?
Select your camera
Set a Keyframe by pressing I and selecting Rotation
Then move some frames forward (by clicking in the Timeline at the bottom)
Now rotate the camera by pressing R+X+3+6+0 and apply by pressing Enter 
(Press X twice if you want to rotate around a local axis instead)
Set another keyframe like in step 2


That's all. Note that the movement won't be linear by default. If you want a linear movement instead, you need to change the interpolation mode of the keyframes. For that, you can have a look at the second part of this answer.
Hope it helps :)